The theory of $p$-adic representations over a $p$-adic local field was developed by J.-M. Fontaine and this has emerged as one of the important areas of research in Arithmetic Geometry. Along with the classical Langlands program, this area of research has led to the $p$-adic Langlands program as part of the larger picture connecting representation theory, number theory and algebraic geometry. The Fargues-Fontaine curve is a geometric object that can be used to study representations of $p$-adic local fields. It has earned the sobriquet of `Fundamental curve in $p$-adic Hodge Theory'. The study of $G$-bundles on the curve, where $G$ is a reductive algebraic group has seen enormous advances and has parallels with the seminal work in algebraic geometry of the study of vector bundles over a compact Riemann surface. The work of Peter Scholze has brought new insights into this rapidly developing area. This field will unravel in the coming years as a tantalizing playground that connects algebra, geometry and number theory. This discussion meeting aims at attempting to understand the recent results as well as to learn the emerging techniques and new problems.
As part of the discussion meeting, we will have ICTS Distinguished Lecture by Prof. Jean-Marc Fontaine
Jean-Marc Fontaine, CNRS and Université de Paris-Sud, France, will deliver a series of lectures introducing the rings that arise in p-adic Hodge theory and the role played by Scholze's theory in the study of the Fargues-Fontaine curve.